Asked by Hannah
1)What is the domain of f/g?
f(x) = x/x+1, g(x) = x^3
all real numbers greater than 1. Am I correct?
2) Find f x g, g x f, and f x f
f(x) = 3sqrt x-1 g(x) = x^3+1
For the f(x) the 3 is little above the sqrt sign.
I do not understand how do fidn these.
f(x) = x/x+1, g(x) = x^3
all real numbers greater than 1. Am I correct?
2) Find f x g, g x f, and f x f
f(x) = 3sqrt x-1 g(x) = x^3+1
For the f(x) the 3 is little above the sqrt sign.
I do not understand how do fidn these.
Answers
MathMate
(1) Not quite, you need to exclude cases where the denominator becomes zero, where the function is undefined.
For f(x), the domain is R for the numerator, and R\-1 for the denominator, since x+1 cannot equal zero as a denominator. In all dom f(x) is R\-1.
For g(x), the domain is simply R.
For f/g, g(x) cannot be zero, so dom g(x) = R\-1,0
The combined domain of f(x)/g(x) is therefore R\0,1, or in interval notation: (-∞,0)∪(0,1)∪(1,∞).
For f(x), the domain is R for the numerator, and R\-1 for the denominator, since x+1 cannot equal zero as a denominator. In all dom f(x) is R\-1.
For g(x), the domain is simply R.
For f/g, g(x) cannot be zero, so dom g(x) = R\-1,0
The combined domain of f(x)/g(x) is therefore R\0,1, or in interval notation: (-∞,0)∪(0,1)∪(1,∞).